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Thursday, September 26, 2013

The multiverse is not a paradigm and it’s not shifting anything.

Google “multiverse paradigm” and you get more than a thousand hits. According to Wikipedia a paradigm “describes distinct concepts or thought patterns”. Unfortunately, the multiverse is pretty much the opposite: There’s no distinct concept, but instead a variety of loosely related properties of existing theories that are being construed to have a common theme which, we are then told, is sign of an impending paradigm shift.

I’m starting to take offense in this forward defense. If the spread of multiversal “thought patterns” is sold as a paradigm shift, everybody opposed to the multiverse is discarded as being stuck in yesterday. It’s only the enlightened who are ahead of their time and understand the significance. I really don’t think there’s any paradigm here and certainly nothing is shifting. To see why, it’s helpful to distinguish two different classes of multiverses that are presently being discussed, usually thrown together.

1. The Multiverse of Disappointed Hopes

Science works by constructing models for real world systems. These models can then be used to understand what happens in the real world, and to make predictions. A theory is a map from a model to the real world. The model should not be confused with the theory itself. The theory is what tells you how to identify properties of the model with the real world. The model is the actual stand-in for the real world system.

Einstein’s General Relativity for example is a theory: it’s a prescription for how to deal with space-time and particles moving in it. A model is the space-time of a star or an approximately homogeneous matter distribution. It’s the theory of General Relativity, but the ΛCDM model. Likewise, there’s quantum field theory, and the standard model. Needless to say, not everybody uses this terminology all the time, but that’s how I want to use it.

Models and theories are not only used in physics and don’t necessarily have to be mathematical. Psychologists have models for human behavior that they apply to patients – the ‘real world’. A drawing is a model, in this case the “theory” that connects it to the real world comes for free with your visual cortex. A story is a model, the “theory” is your knowledge of the language that relates letters to real world objects or actions. And so on. The merit of mathematical models is that they have a very strict quality control, which is self-consistency.

And then there are toy models.

Toy models are models that do not have real world counterparts. It’s drawings of creatures that don’t exit or stories of people that have never lived. They’re playgrounds of creativity that can teach us lessons about the theory, which is why studying toy models is a very common and often fruitful exercise. There’s an infinite amount of such toy models. You could say there’s a whole multiverse of them, all these toy models that don’t map to any part of the universe we know. Asking whether what they describe is real is like asking if Harry Potter really exists because a story has been written about him. The difference between fantasy novels and physicist’s toy models is the size of the interested audience, but in spirit they’re the same exercises in creativity.

So, sure there are models that don’t describe the real world, in physics as well as in painting. That’s because mathematical consistency alone does not imply a model describes what we observe, much like using English does not imply you talk about real people. Additional requirements are needed besides consistency to construct a useful model, and these requirements are always agreement with observations, though this isn’t always explicitly phrased this way. When we assume Lorentz-invariance or renormalizability or absence of ghosts, these are physical requirements ultimately based on our experience.

This means a multiverse that you can get rid of by adding the requirement that the model needs to describe observation is neither new, nor surprising, nor something to worry about. It just means that mathematical consistency of whatever theory it is you’re dealing with is not sufficient to make a particular prediction. The string theory landscape is a multiverse of this type. The only reason people talk about this now is that many of them had been hoping string theory would make some requirements that one needs in the standard model unnecessary. Alas, these hopes were disappointed, though the last word might not be spoken yet.

Does it make sense to instead talk about probability distributions over the models you get when you refuse to use existing ties to observations, here specifically the values of certain parameters? No. Because that’s cherry picking the observations you want to neglect.

In the construction of the model there always enter many other observations that are being neglected if one considers such probability distributions, such as the number of (large) dimensions, Lorentz-invariance, or the existence of space-time to begin with – these are not requirements of mathematical consistency, these are physical requirements based on observations. If you wanted to be serious with asking for the probability of particular models, you should sample over all models, in the end over all that is mathematically consistent. You’d be left with Tegmark’s mathematical multiverse. And in that mathematical universe you’d have replaced the question “Which model describes the real world?” with “Where are we in the mathematical universe?” You don’t gain anything.

Once you have seen the power of mathematical models to describe natural systems, it is natural to ask if there is a mathematical model that describes “everything” we see. I believe there is. But people who search for a “theory of everything” today mean more than that. They want in particular a theory that delivers the parameters in the standard model. But even if that would be achieved, we would still have to use other axioms that are ultimately based on observations. So while it is worthwhile to try to find a simpler model that reduces the number of axioms, including values of parameters, we can never avoid using input from observation. If we do, we’ll end up with a multiverse which just tells us that mathematical consistency isn’t sufficient.

So if you have a multiverse that can be eliminated by the requirement that the model is consistent with observation, this isn’t a paradigm shift, it’s just disappointed hopes.

2. The multiverse package deal

But there’s a different type of multiverse, one that you cannot get rid of by requiring match to observation. It’s the case in which a theory applied to a model that describes a real world system necessarily maps into a space that is larger than what we observe. Eternal inflation and the many worlds interpretation of quantum mechanics are of this type. Or, more mundanely, there is nothing in ΛCDM that predicts the universe just ends beyond the distance that we can (presently) observe, so you have a multiverse beyond our observations.

This opens a can of interpretational worms because we can now endlessly discuss whether the not observable images of the map are real or not. Personally, I find this a rather fruitless debate about the meaning of the world ‘real’. To me a model is a tool to describe the real world and if it does that, and if it’s an improvement over other models, I don’t care if there are mathematical elements in the model that don’t correspond to real world observables. Mathematics is full of structures that for all we know don’t correspond to anything we observe anyway. I don’t see a reason why we must be able to observe them all.

But, no, I don’t think you should just shut up and calculate. Because we might be mistaken in thinking that what the theory predicts beyond our observable universe is indeed unobservable. Maybe we just haven’t asked the right questions and there are ways to observe it after all.

So it’s an interesting feature that theories can display, but it’s certainly not a new concept. There’s been a century of discussion about the presence of mathematical objects in quantum mechanics that for all we presently know are fundamentally non-observable. So if that’s a paradigm shift it’s one that has already happened long ago.

“Are there aspects of observable reality, i.e. the universe, that can be explained by multiversality, but not otherwise?”

It is fruitful to look at the answers to gauge the depth of the existing arguments in favor of the multiverse:

“Yes – one is the apparent indeterminism of quantum mechanics, despite its deterministic equations.”

Wilczek claims here the apparent indeterminism of quantum mechanics can be explained by the many worlds interpretation but not otherwise. That’s an objectionable claim, in particular because the qualifier didn’t include anything about locality.

“Yes – the outrageously small, but non-zero, value of the dark energy density.”

Here he is claiming that there is no other way to explain the measured value of the dark energy density than anthropic reasoning and that anthropic reasoning necessarily implies a multiverse. There are many people who would object on the former and the latter is manifestly wrong. You don’t need a multiverse to do anthropic reasoning, see my post Misconceptions about the anthropic principle.

“Yes – the opaque and scattered values of many standard model parameters that are not subject to the discipline of selection.”

An interesting answer because it is phrased to suggest that the values of the standard model parameters are scattered to begin with. Even if they were however that wouldn’t force us to believe that any possible distribution of values actually exists in a more meaningful sense than Harry Potter exists.

Taken together, these answers tell you aptly just how weak the case for a multiverse really is.

Summary

We should distinguish between multiverses that you can eliminate by adding axioms to the theory that tie the model to the real world, and those that you can’t eliminate this way. The string theory landscape is of the former type, you “just” have to find the right vacuum, and good luck with finding that. Eternal inflation and the many worlds interpretation are of the latter type. In this case you get more than you asked for. One can interpret this type of multiverse as a calculation device which might have its uses. It might also turn out that these multiverses aren’t unobservable after all, so these ideas certainly merit some investigation. In any case however, there’s no paradigm shifting here.

So what does this mean? We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory.

Think of the photon as a waveform in space, analagous to a seismic wave deep in the ground. It goes through both slits and interferes with itself. However when you detect it at one slit you perform a wavefunction-wavefunction interaction that operates akin to an optical Fourier transform. The photon is transformed into a dot at that slit so it goes through that slit only, and there is no interference. When you detect it on the screen you perform another wavefunction-wavefunction interaction that again operates akin to an optical Fourier transform. Hence you get a dot on the screen. No magic, no mystery, and no many-worlds is required.

You wrote "It just means that mathematical consistency of whatever theory it is you’re dealing with is not sufficient to make a particular prediction. The string theory landscape is a multiverse of this type. The only reason people talk about this now is that many of them had been hoping string theory would make some requirements that one needs in the standard model unnecessary. "

If we give string theory all the requirements one needs to put into the Standard Model, can it give us a unique answer? Or are there many answers that differ in between say 100 TeV and the string scale, even though they all agree with the Standard Model at the current level of experimental precision?

If there are many answers, i.e., the Standard Model under-determines the String Model, isn't that a different flavor of multiverse?

Sabine, a very enjoyable reading and analysis... a sensible stance as philosophy too. I too saw the need to reason out the multiverse and manyworlds distinction, obviously. But to me if it is the case of what nature does in some location it always was and will always be the case also. (at least it can be this way intermittently over a span of space and time)... your English is better than mine! You would sell a lot of books, and helpful ones too, if you expanded this to a popularization on physics - but the physics itself is more important. Each of us in a sense is this paradox of a manyworld wishing for some change of mystery to come. I comment to you after just writing a chapter with local color and clarity (will put it in my fb notes about a character Jubal) which I hope let me see right away the clarity and coherence of your essay for the depth it is in an honest assessment. We all know the anthropic principle is a holding one and a cop out.

For some reason "green as Envy," kept coming to mind(not even sure what that was suppose to mean)?:)Merkel's 3rd term? Pretty amazing for a minority government that has to now work with the social left?

Perhaps, such distinction as multiversial may arise now as questions of what is qualitative versus quantitative, by examination? Can you do away with Genus figures and be happy? Can abstraction help to form new ideas?

Bee, clever and entertaining rundown of the issues. I love all that Merkel stuff (BTW folks she is not "conservative" by USA standards!) One point regarding models in general: there is an intuitive pressure that many can't resist, that "realistic" models just have to be true. Hence, e.g. the push to believe that the wavefunction exists and just has to keep on evolving, despite the evidence to the contrary of unpredictable, exclusivising outcomes.

But I think that the universe is not "realistic", not like classical EM or a draftsman's drawing. It just isn't like that no matter how much most scientists (?) want it to be like that. So there really isn't an answer to, what is one entangled particle like before it's measured etc or does the WF "really exist" at first and then "just vanish everywhere else" when we make a measurement. The world is relational and not locally realistic.

As for measurement and collapse, I think that things happen the way they seem to: nuclei decay at specific moments and there are no other cats in other worlds, an atom in a detector just by chance can grab enough energy to make the transition and take the energy out of action for any other atom, etc. Perhaps it's part of the energy-time uncertainty relation? But in any case it is silly to keep forcing classical ideas on things.

johnduffieldblog: I'm sorry but that concept does not remove the mystery. You have an extended WF and the problem is to explain how it can end up of any of *many* possible final positions. Furthermore, part of the weirdness of quantum mechanics is that you can get multiple outcomes (like, muon lifetimes) from an (AFAWK) identical starting point. That is just not deterministic. Any mathematical process is deterministic, so-called random functions actually describe the space of outcomes and do not *produce* varying outcomes by themselves.

1. A paradigm is an overarching conceptual framework for an entire field of study. Thus the theory of biological evolution is the paradigm for biology and provides a conceptual framework for the various theories and models of that field. The term paradigm is often used incorrectly to mean any new and unorthodox idea, theory or model, regardless of conceptual basis and scope.

2. I am very glad to see you question Wilczek on his three specious reasons for making a multiverse model mandatory. I was shocked when I read that part of the paper. He is supposed to be a deep thinker and highly qualified physicist, and yet when it comes to fashionable ideas like string theory/SUSY and the multiverse, he and many others seem to lose their scientific compasses.

Well said Robert. I would put it more strongly and say guys like Wilczek are harming physics by peddling woo like that. The public will end up thinking they shouldn't fund physics if that's what physicists come up with.

Neil: sure, it doesn't answer everything, but that concept surely knocks the many-worlds fantasy on the head.

Good point, I was somewhat careless on that. No, I don't think it's a different type of multiverse it just means you need observations that you haven't yet been able to make. It's like having the standard model Lagrangian with the mass of the top quark missing. Nobody would call that a multiverse. To begin with, you never know the parameters exactly anyway because there's always measurement uncertainty. So if that was a multiverse, we'd always have a multiverse in the trivial sense that there are infinitely many real numbers in any finite interval, no matter how good the precision. Best,

Yes, I would agree on 1). Re 2) I too found the Wilczek paper disappointing though it's so strangely patched together that I suspect there might have been a deadline pressure having something to do with the outcome. It starts pretty good and is nicely written, but it reads like he run out of steam after a few pages and then instead copied a summary of some other recent work. Best,

For what it's worth, Max Tegmark is careful to define the four levels of multiverses he discusses. (I would use other terminology, but at least he defines clearly what he means and sticks to it.) Also, the multiverses he talks about are not hypotheses, but rather predictions of other theories. Sure, the theories might be wrong, but in principle can be ruled out (not necessarily via arguments involving multiverses).

1 Beyond our cosmological horizon: GR allows us to envisage an early universe where energy-density/pressure was very high, much as it is down near a black hole where gravitational time dilation is high. So if the universe expands even at some sedate pace, any observers within that universe would assert that the expansion was extremely rapid. Like inflation. Only if the universe was infinite, it couldn't expand. But it does.

2 Universes with different physical constants: this universe has different physical constants. The fine structure constant is a running constant, the coordinate speed of light varies in a gravitational field, invariant mass varies, the cosmological constant isn't constant, and so on.

3 Many Worlds: see comment1 above.

4 Ultimate ensemble: the universe is not made of mathematics.

All this multiverse stuff is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.

Less than 100 years ago scientists discovered that most of what we could observe was contained within one galaxy, and there were at least 100 billion other galaxies at larger distances. The fundamental physics in each of these galaxies appeared to be exactly the same, and that hypothesis has been validated over the subsequent decades.

Is it so unthinkable that the same type of discovery process could be repeated? Perhaps, once again, what we observe is all part of one metagalactic object, and there are countless numbers of these objects, and the fundamental physics is exactly the same in each one.

You ask: Where would this hierarchy end? I answer: Why would you assume that there must be an "end"?

For me the multiverse is a political phenomenon of decadent and religious physics of current era. It's a consequence of the fact, that the theorists adhere on (the postulates of) their beloved theories so much, they're willing to attribute any deviation from them to ultramundanne effects, i.e. the multiverse instead of to possible violation of these theories.

So for example instead of looking for falsification of Big Bang model they're looking for additional multiverses, which are fulfilling the Big Bang model.

/*..Are there aspects of observable reality, i.e. the universe, that can be explained by multiversality, but not otherwise..*/

You can always explain multiversality with more general model. Existing theories are just four - ten dimensional: the physicists still didn't started to think about actual dimensionality of our Universe, which is apparently much higher. In AWT the universe is infinitely-dimensional and such a model indeed doesn't require to introduce multiverse at all.

But the contemporary physicists apparently think, that the Universe is low-dimensional in the same way, like their formal reductionist theories - after then they're indeed face the excessive degree of freedom during fitting of their theories into reality. But it's just because they have no more general theory developed yet (and the dense aether model is not good enough for them).

And there shall in that time be rumours of things going astray, and there will be a great confusion as to where things really are, and nobody will really know where lieth those little things with the sort of raffia work base, that has an attachment…at this time, a friend shall lose his friends’s hammer and the young shall not know where lieth the things possessed by their fathers that their fathers put there only just the night before around eight o’clock...

/* ..If an object can expand then it is obviously quantifiable and thus not infinite .. */

It's true, that the steady-state infinite universe model disfavors the expansion, but because our visibility scope in it is limited, the the observable portion of Universe can still exhibit some transform as a whole. IMO we don't observe such an transform, as all phenomena (red shift, dark energy and CMBR anisotropy) can be explained with geometry of light scattering in it.

I also think an infinite universe can expand. Someone, I think it was Cantor, or perhaps Hilbert, showed that there are infinite sets of different sizes (some are bigger than others).

More basically than that, I can conceive of an infinite universe containing all its matter in a regular lattice with a spacing of x dimensional units between adjacent particles. (A toy model.) Now let x increase with time (all the particles move farther apart). That is how we define expansion in our universe, is it not?

Also, there is the example of Cantor's Hotel. It has as many rooms as there are positive integers, but even when it is full it can accept new guests. To make room, all the quests move into even-numbered rooms. The guests in room 1 move into room 2, those in room 2 move into room 4, room n moves into room 2n, and so on, leaving all the odd-numbered rooms free for occupancy.

I think infinite sets can be infinitely weird and normal intuition does not apply.

Philip: an infinite universe can't expand because the pressure is counterbalanced at all locations.

See Phil Plait's blog. He said dark energy acts like pressure. This is often described as negative pressure, but that's only because gravity pulls. The cosmological constant is "the energy density of space", and it's positive. Space has a positive volume, and energy = pressure x volume. So the pressure is positive too.

Early theoretical chemistry calculated organic molecules' enthalpies of formation within a hartree or so. A chemical bond is 3 ev maximum. Look up a hartree. For less than a textbook's price, HyperChem Lite calculates bond lengths and angles within 2% of crystal structures. Enthalpies of formation snug measurement. Five minutes of "crude" mm+ iteration does it.

Physics' 40 years refining string and quantum gravitations; standard model anomalies, violations, and breakings; dark matter; and showing GR is not complete, offer NOTHING empirical. Physics is 1) stuck in a local minimum, or 2) has a defective founding postulate. There is no escape by doing more of the same. mm+ has a molecular symmetry defect. The vendor confirms that failure, but nobody else has complained. Naughty me.

I propose five classes of geometric tests of spacetime geometry targetting assumed exact vacuum mirror symmetry toward matter. Physics boldly rejects the concept: "It contradicts accepted theory." So does observed reality. What can physics lose by loading existing apparatus with chemistry? Angela Merkel is a physical chemist. Her success knows "within a hartree" is not good enough, however easy and popular it is to obtain.

John_____, an infinite universe can indeed expand in the sense of benchmark locations like galaxies that see uniform CMBR will all get farther and farther apart. The pressure issue is all relative to a given object, no other *net* pressure means that gravity or DE can act to attract and repel them just as before. (Also, REM the Newtonian approximation of the outer reference galaxy being just under the continued infinite series of outer shells with gravity all canceling out.)

However, an energy paradox can be formed from this concept. We can imagine a model universe with each reference object (equivalent to a galaxy) connected by elastic bands like a "jungle gym" (x, y, z axes in all directions and repeated indefinitely without an edge. Well, the tension in the bands all cancels out for a given object (vector cancellation of pulls.) So, the objects can continue to expand just as if they were free-floating. However that causes a problem with conservation of energy. (See my blog post at http://tyrannogenius.blogspot.com/2010_03_01_archive.html.)

Oops I fudged that a bit - pressure does have its own contribution to effective gravitational mass but that just alters the magnitude, it still does not prevent a deceleration/acceleration parameter from applying to an infinite universe. If our universe is expanding past the break even Omega value then it should be hyperbolic and in simplest topology, literally infinite (altho I suppose that DE and vacuum variations etc makes all this dicey.)

Neil: IMHO it's best to consider space alone. You know how a balloon analogy is often employed? The balloon skin is elastic. To expand the balloon you pump air in, effectively adding energy. Alternatively you can make the balloon skin weaker, whereupon it expands without any conservation-of-energy issues. For a better analogy move on to the raisins-in-the-cake, but forget about the raisins.

Note that big-bang cosmology says the universe started small. An infinite universe contradicts that. You can't have your cake and eat it.

An expanding infinite universe is Escher's hyperbolic tesselation of a circle. Draw a larger radius concentric circle about the original, erase the original circle's boundary, expand. Ditto a ball's volume, etc.

An infinite universe can expand though you have to be careful with defining what you mean with expansion. It's normally taken to mean a 'local' expansion with respect to fixed 'yardsticks'. For example, the space between galaxies increases relative to the size of the galaxies themselves, irrespective of whether or not there's an infinite amount of galaxies. And that is not theory but an observational fact. Best,

Sorry, I realize the last sentence of my previous comment could be misunderstood. This expansion is well described by General Relativity of course. I meant that there's no ambiguity in this prediction.

Sabine what you write about String theory landscape is not quite correct in the sense that there is a real dynamical mechanism which allows you to realize the string vacua (i.e. it is not just a mathematical landscape).

To make it concrete suppose in a point of an eternally inflating space the corresponding flux which parametrizes the Calabi-Yau suddenly changes; the end result of this is the transition to another string vacuum i.e. another universe is created.

This is a key point and this is why String landscape is seen in conjunction with eternal inflation. I.e. String landscape provides the possibilities and eternal inflation permits you to realize these possibilities.

/*..expansion is well described by General Relativity of course. I meant that there's no ambiguity in this prediction..*/

The dense aether model explains expansion of Universe with scattering of light waves at the density fluctuations of vacuum (which are known as a CMBR noise). This leads to change of light waves with distance from ANY observer in this system. This leads to famous Einstein's expansion paradox: the space-time expands globally, although it nowhere expands locally.

Such a situation can be modeled with scattering of ripples at the water surface. One observer sitting at the water surface would see, that the wavelength of surface ripples is shrunken at the place of remote observer. But this distant observer will see exactly the same about first observer. Both perspectives are perfectly equivalent, so there is no expansion of space-time at all from global perspective. But because this global perspective is not available for any observer, we are forced to think about two multiverses with different reference frames, in which each of observer is residing.

IMO the Einstein's expansion paradox is impossible to explain without dense aether model.

Why would it change? Or let me ask the question differently. Suppose somebody found a vacuum that fits with all observed parameter values/gauge symmetries and so on. Do you think anybody would care about the rest? Best,

/* Suppose somebody found a vacuum that fits with all observed parameter values/gauge symmetries and so on. Do you think anybody would care about the rest? */

It's a question of economy of such prediction too. The people are looking not only for more exact solutions, but for more effective solutions too. I presume, they're willing to continue with it, until we would be willing to pay them for it.

Before moduli stabilization via fluxes there was the hope that the theory will stabilize the moduli in a way that the end result would resemble our type of vacuum. This together with a vacuum selection principle (maybe derived from some internal consistency condition of the theory) would allow us to further pinpoint our vacuum via a top-down approach.

After KKLT and flux compactifications milestones though(the notorious 10^500 vacua etc)it was realized that such a possibility is very difficult to be realized if not impossible.

Of course even now if they could find the exact string vacuum we are living (via a bottom-up approach) would be extremely important for the theory and in String phenomenology considerable progress has been made in that direction. But of course this doesn't mean that there is no multiverse (at least according to the current state of affairs you never know what future research might reveal).

I don’t think so (if I understand your question correctly). If you don’t stabilize the moduli you get a bunch of massless scalar fields with undetermined VEVs. The VEVs of these scalars on the other hand are related to the values of specific parameters (e.g. coupling constants) of the effective theory in the 4 uncompactified dimensions; you won’t be able to make predictions if you don’t determine the VEVs of the moduli. Basically you don’t have a model to work with.

This is perhaps a late comment for this blog, but I hope, you Bee, or someone else on this blog would respond. I am somewhat sympathetic to the idea of multiverse in the cosmological sense but not at all in the quantum mechanics (Everett) sense. For QM it seems to me that this is total copout because we do not understand QM . My reasoning is this. This idea in QM is so vague and arbitrary that perhaps it cannot even be called science. Suppose a professor asks his graduate student to do a QM expt next morning. If the student comes to work early then the universe splits. If the student feels lazy that morning and does not do the expt then the universe does not split!!! After the experiment is done with say a billion electrons or photons the final result is completely predictable. Any other graduate student will get the same answer. Thus all the split universes have to conspire to give the same final answer! If the argument is that the universe is split already in heavens before any experiment is done and you are just choosing the branch (by free will?!!), that argument would be too religious and unscientific (Not that I have any objection to that. I am not atheist!). I am puzzled why some distinguished scientists would believe in Everett multiverse at all.